Rewrite the expression in the form $z^n$. $\sqrt[5]{z^4\,z^{^{\scriptsize -\dfrac32}}}=$
Solution: $\begin{aligned} \sqrt[5]{z^4\,z^{^{\scriptsize -\dfrac32}}}&=\sqrt[5]{z^{^{ 4\scriptsize-\dfrac32}}} \\\\ &=\sqrt[5]{z^{^{\scriptsize \dfrac52}}} \\\\ &=\left(z^{^{\scriptsize \dfrac52}}\right)^{^{\scriptsize\dfrac15}} \\\\ &=z^{^{\scriptsize \dfrac52\cdot\dfrac15}} \\\\ &=z^{^{\scriptsize \dfrac12}} \end{aligned}$